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Journal of Graph Theory, ISSN 0364-9024, 09/2017, Volume 86, Issue 1, pp. 78 - 91
A noncomplete graph Γ is said to be (G, 2)‐distance transitive if G is a subgroup of the automorphism group of Γ that is transitive on the vertex set of Γ, and... 
20B25 | 2010 Mathematics Subject Classification. 05E18 | permutation group | 05E18 | 20B25. 2‐distance transitive graph | 2‐arc transitive graph | 2-arc transitive graph | 20B25. 2-distance transitive graph | MATHEMATICS | 2-distance transitive graph | 2010 Mathematics Subject Classification
Journal Article
Combinatorica, ISSN 0209-9683, 8/2019, Volume 39, Issue 4, pp. 933 - 960
This paper initiates a limit theory of permutation valued processes, building on the recent theory of permutons. We apply this to study the asymptotic... 
60G57 | 60C05 | Mathematics, general | Mathematics | 05E18 | Combinatorics
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2018, Volume 38, Issue 3, pp. 853 - 865
The distinguishing number (index) ) ( ′( )) of a graph is the least integer such that has a vertex labeling (edge labeling) with labels that is preserved only... 
distinguishing index | 05E18 | distinguishing number | lexicographic | 05C15 | Distinguishing number | Distinguishing index | Lexicographic | MATHEMATICS
Journal Article
Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2020, Volume 40, Issue 3, pp. 875 - 884
The distinguishing number (index) ) ( ( )) of a graph is the least integer such that has an vertex (edge) labeling with labels that is preserved only by the... 
distinguishing index | unicyclic graph | automorphism group | tree | 05E18 | distinguishing number | 05C15 | 05e18 | 05c15
Journal Article
Combinatorica (Budapest. 1981), ISSN 1439-6912, 2015, Volume 36, Issue 4, pp. 371 - 393
Let A be an abelian group and let ι be the automorphism of A defined by: ι: a ↦ a−1. A Cayley graph Γ = Cay(A,S) is said to have an automorphism group as small... 
20B25 | Mathematics, general | Mathematics | 05E18 | Combinatorics | MATHEMATICS | PERMUTATION-GROUPS | SCHUR RINGS | CYCLIC GROUPS | REGULAR REPRESENTATIONS
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 6/2019, Volume 23, Issue 2, pp. 285 - 293
We classify the unimodular equivalence classes of inclusion-minimal polygons with a certain fixed lattice width. As a corollary, we find a sharp upper bound on... 
Polytopes | Convex lattice polygons | Secondary 05E18 | Convex lattice | Primary 52B20 | 52C05 | Mathematics | Combinatorics | Lattice width | MATHEMATICS, APPLIED
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 3/2018, Volume 59, Issue 2, pp. 331 - 362
We consider the orientation-preserving actions of finite groups G on pairs $$(S^3, \Gamma )$$ (S3,Γ) , where $$\Gamma $$ Γ is a connected graph of genus... 
57M60 | Computational Mathematics and Numerical Analysis | Mathematics | Extendable action | 57M15 | 05E18 | Symmetry of 3-sphere | Combinatorics | Symmetry of graph | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | SURFACES | Graphs
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 3/2018, Volume 59, Issue 2, pp. 451 - 460
For any given finite group, Schulte and Williams (Discrete Comput Geom 54(2):444–458, 2015) establish the existence of a convex polytope whose combinatorial... 
Automorphism | Group | Computational Mathematics and Numerical Analysis | Graph | Convex polytope | Mathematics | 05E18 | 52B15 | Combinatorics | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | GRAPHS | Automorphisms | Combinatorial analysis
Journal Article
Experimental Mathematics, ISSN 1058-6458, 01/2017, Volume 26, Issue 1, pp. 54 - 61
We study surface subgroups of groups acting simply transitively on vertex sets of certain hyperbolic triangular buildings. The study is motivated by Gromov's... 
periodic apartment | surface subgroup | hyperbolic building | Primary: 05E18 | Secondary: 20F67 | MATHEMATICS | SURFACE SUBGROUPS | 51E24
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2019, Volume 100, Issue 1, pp. 131 - 147
A classical result of Honsberger states that the number of incongruent triangles with integer sides and perimeter $n$ is the nearest integer to $n^{2}/48$ (... 
2010 Mathematics subject classification | primary 52B05 | secondary 05A17 | 05E18 | 05A10 | orbit enumeration | MATHEMATICS | dihedral groups | integer polygons | perimeter | TRIANGLES | enumeration
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 04/2017, Volume 49, Issue 2, pp. 320 - 330
In his doctoral thesis, Snover proved that any binary (m,256,δ) code is equivalent to the Nordstrom–Robinson code or the punctured Nordstrom–Robinson code for... 
20B25 | 05C25 (secondary) | 05E18 (primary) | 94B05 | MATHEMATICS | REGULAR CODES | GOETHALS | BINARY | TRANSITIVE CODES | Z-LINEAR CODES | PREPARATA | KERDOCK | SYMPLECTIC SEMIFIELD PLANES
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 8/2019, Volume 87, Issue 8, pp. 1815 - 1838
Journal Article
Designs, Codes and Cryptography, ISSN 0925-1022, 5/2018, Volume 86, Issue 5, pp. 1095 - 1111
Journal Article
Natural computing, ISSN 1572-9796, 2017, Volume 18, Issue 3, pp. 445 - 458
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 9/2018, Volume 48, Issue 2, pp. 179 - 225
We establish, for the character table of the symmetric group, the positivity of the row sums indexed by irreducible characters, when restricted to various... 
Character tables | Symmetric power | Mathematics | 20C30 | Convex and Discrete Geometry | Exterior power | Conjugacy action | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Plethysm | 05E18 | Combinatorics | Computer Science, general | Ramanujan sum | 20C05 | 20C15 | 06A07
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 8/2018, Volume 48, Issue 1, pp. 157 - 178
In recent work we constructed two new near octagons, one related to the finite simple group $$\mathrm {G}_2(4)$$ G2(4) and another one as a sub-near-octagon of... 
Distance-regular graph | 51E12 | Mathematics | Finite simple group | 51E25 | Generalized polygon | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Commuting involutions | 05E18 | Combinatorics | Computer Science, general | Near polygon
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 3/2016, Volume 20, Issue 1, pp. 21 - 58
The “classical” parking functions, counted by the Cayley number (n+1) n−1, carry a natural permutation representation of the symmetric group S n in which the... 
diagonal harmonics | 05E10 | q, t -Catalan numbers | rational Catalan numbers | Shuffle Conjecture | 05E05 | rational parking functions | Mathematics | 05E18 | Combinatorics | q, t-Catalan numbers | MATHEMATICS, APPLIED | COMPACTIFIED JACOBIANS | STATISTICS | CONJECTURES | COMBINATORIAL FORMULA | CONTINUOUS FAMILY | CHARACTER
Journal Article
Journal of algebraic combinatorics, ISSN 1572-9192, 2018, Volume 50, Issue 2, pp. 143 - 163
An m -Cayley graph $$\Gamma $$ Γ over a group G is defined as a graph which admits G as a semi-regular group of automorphisms with m orbits. This generalises... 
m -Cayley graph | Symmetric graph | Mathematics | 20B25 | Double-coset graph | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | 05E18 | Combinatorics | Computer Science, general | 05C25 | Simple group | m-Cayley graph | DIHEDRAL GROUPS | MATHEMATICS | AUTOMORPHISMS | TRANSITIVE GRAPHS
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 9/2016, Volume 20, Issue 3, pp. 609 - 621
We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small m–Schröder paths and give a... 
cyclic sieving phenomenon | Narayana numbers | Schröder paths | Mathematics | 05E18 | Combinatorics | 05E99 | increasing tableaux | jeu de taquin | Schroder paths | MATHEMATICS, APPLIED | PROMOTION | SCHRODER NUMBERS | JEU
Journal Article
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